Question

A 123-cm-long, 5.00 g string oscillates in its n = 2 mode with a frequency of 200 Hz and a maximum amplitude of 4.50 mm.

What is the tension in the string?

Answer 1

Please explain what you mean by the n=2 mode. Does it have a standing wave with a node in the middle? If so, the wavelength of the traveling waves that form the standing wave is 123 cm. Get the wave speed c from
c = (wavelength)*(frequency)
You already know the frequency.

The wave speed can be used to solve for the string tension, T

c = sqrt [T/(mass per length)]
= sqrt(T*L/m)

The amplitude does not affect the answer.

I suggest using mass in g and length in cm. The answer (T) will then be in dynes.
10^7 dynes = 1 Newton